Stochastic tube MPC with state estimation |
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| Authors: | Mark Cannon Qifeng Cheng Basil Kouvaritakis Sa?a V Rakovi? |
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| Affiliation: | 1. Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, United Kingdom;2. Institute for Automation Engineering, Otto-von-Guericke-Universität Magdeburg, Germany;1. Oxford University, St. Edmund Hall, Oxford, UK;2. Oxford University, Department of Engineering Science, Oxford, UK;1. Dipartimento di Automatica e Informatica, Politecnico di Torino, Torino, Italy;2. Automatic Control Laboratory, Swiss Federal Institute of Technology, Zurich, Switzerland;3. Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA, USA |
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| Abstract: | An output feedback Model Predictive Control (MPC) strategy for linear systems with additive stochastic disturbances and probabilistic constraints is proposed. Given the probability distributions of the disturbance input, the measurement noise and the initial state estimation error, the distributions of future realizations of the constrained variables are predicted using the dynamics of the plant and a linear state estimator. From these distributions, a set of deterministic constraints is computed for the predictions of a nominal model. The constraints are incorporated in a receding horizon optimization of an expected quadratic cost, which is formulated as a quadratic program. The constraints are constructed so as to provide a guarantee of recursive feasibility, and the closed loop system is stable in a mean-square sense. All uncertainties in this paper are taken to be bounded—in most control applications this gives a more realistic representation of process and measurement noise than the more traditional Gaussian assumption. |
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